-
Pergamon 0305-0548(95)00047-X
Computers Ops Res. Vol. 23, No. 4, pp. 393-404, 1996 Copyright
1996 Elsevier Science Ltd
Printed in Great Britain. All rights reserved 0305-0548/96 $15.0
+ 0.00
EFF IC IENCY OF TRUCKS IN ROAD CONSTRUCTION AND
MAINTENANCE: AN EVALUATION WITH DATA
ENVELOPMENT ANALYS IS
Lennart Hjalmarsson* and James Odeck ~ Department of Economics,
Goteborg University Grteborg, Sweden
Scope and PUrlmSe--This study investigates the efficiency of
trucks in road construction and road maintenance. Efficiency is
defined relative to a benchmark in the form of best-practice
trucks. For every truck, not serving as a best-practice benchmark
itself, its benchmark is derived within the framework of Data
Envelopment Analysis (DEA). With the same approach distance
measures i.e. efficiency scores, are calculated. A main attraction
with this approach is that it is possible to handle multiple
input-multiple output technologies. The efficiency scores measure
different aspects of a truck's performance relative to its
best-practice benchmark (potential input saving, output augmenting
etc). We shall calculate efficiency at the production unit level
(the truck) and then, since the choice of output variables may be
controversial, compare the stability of efficiency rankings between
different choice of output definitions. Further, we shall
investigate the impact of other factors such as the vintage year of
the truck, make and model of the truck and its area of operation.
The data set consists of heavy trucks, owned and operated by the
Norwegian public roads administration.
Abstract--This paper focuses on the performance of trucks
involved in road construction and maintenance, and operated by the
regional agencies of a national public roads administration. The
performance is evaluated from the productive efficiency point of
view. The framework is that of a deterministic non- parametric
(DEA) approach to efficiency measurement. In this context several
important issues are addressed: efficiency ranking and distribution
among trucks, the importance of an appropriate output measure,
impact of regional characteristics and the significance of the make
and model of the trucks.
1. INTRODUCTION
In this paper we evaluate the performance of heavy trucks, owned
and operated by the Norwegian public roads administration (PRA)
from the point of view of productive efficiency.
PRA is responsible for approximately 40% of all road
construction and 80% of road main- tenance in Norway. It is
subdivided into 19 branches (or agencies) each performing road
construction and maintenance within its assigned region. Each
branch owns a number of machines that are used in its activities in
the region and are orgainzed as an entity (office). This is done to
ensure adequate machinery and material supplies for the
construction and maintenance units. The fleet of machines comprises
heavy trucks, tractors, excavators etc. There is a total of 50
machine groups of which "heavy trucks" is one of the 3 largest.
Heavy trucks are used both in road construction (in transportation
of mass from rock blasting, transport of asphalt, sand etc.) and in
road maintenance, notably snow plowing.
In the recent years, the public sector in Norway, as in many
other countries, has been criticized for not performing as well as
it should in providing services. A recent report by a government
commission shows that there is a great potential for increasing
efficiency in providing infrastructural services. One way to
realize the potential is to identify the causes of inefficiency
within a sector. A
*Lennart Hjalmarsson is currently Professor of Economics at
Goteborg University, Sweden. His main research fields are
industrial economics, productivity, production theory, energy
economics and deregulation. His list of publications include 12
monographs and edited books, more than 20 articles in international
journals and a large number of contributions to edited books.
S James Odeck is currently economist with the Norwegian Public
Road Administration in Oslo, Norway. He holds his Ph.D. from
Goteborg University, Sweden.
393
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394 Lennart Hjalmarsson and James Odeck
first step may then involve an evaluation of micro units of the
sector, e.g decision making units of the road sector, and find out
how these units perform. By relating the performance of units to
one another and identifying the most efficient units, benchmarks or
yardsticks are provided. If such efficiency scores are made public,
the inefficient units may be encouraged to adopt the technology of
the efficient ones and hence increase efficiency in the sector as a
whole (so called yardstick competition).
In this study efficiency measures for the utilization of trucks
in road construction and main- tenance are computed within the
framework of a deterministic non-parametric model, Data Envelopment
Analysis (DEA). We shall calculate efficiency at the production
unit level (the truck) and then compare the stability of efficiency
rankings between different output measurements. Further, we shall
investigate the impact of other factors such as the vintage year of
the truck, make and model of the truck and its area of operation.
Efficiency calculations and the subsequent comparisons are done for
all the 72 units, spread all over the country and performing the
same set of tasks.
Applications of DEA in the measurement of efficiency are now
abundant. For a more extensive bibliography of DEA studies, see
[1]. Applications on the road sector are, however, rare. To our
knowledge the closest one gets to the road sector in this extensive
literature is [2] on ferry services, and [3] on maintenance
patrols.
The rest of this paper is organized as follows: Section 2
presents the methodology and Section 3 the data along with
discussions on the different output measures. The empirical results
are presented in Section 4, while concluding remarks are in Section
5.
2. METHODOLOGY
The DEA method is closely related to Farrell's original approach
[4] and should be regarded as an extension of this approach
initiated by Charnes et aL [5] and related work by F~re et al. [6].
In this approach the efficiency of a micro unit is measured
relative to the efficiency of all the other micro units, subject to
the restriction that all micro units are on or below the
frontier.
The Farrell measures are illustrated in Fig. 1 where a one input
(x) and one output (y) production activity for which statistical
data are available (e.g in cross-sectional form) is assumed. The
frontier technology with variable returns to scale is XAABCD and
the frontier with non- increasing returns to scale is OBCD. The
constant returns to scale (CRS) frontier is the ray from the origin
through point B.
In measuring efficiency we adopt the system of efficiency
measurement introduced in [7]. This system is a generalization of
Farrell's measures to a variable returns to scale (VRS) technology.
The efficiency measures for any unit in K in Fig. 1 are given
as:
(i) E1 = Xj/XK, input saving technical efficiency (VRS) (ii) E2
= Yk/YL, output increasing technical efficiency (VRS)
(iii) E3 = XI/XK, gross scale efficiency (input saving when
(CRS)) (iv) E4 = E3/E1 = XI/X~, pure scale efficiency (input
corrected) (v) E5 = E3/E1 = YL/YM, pure scale efficiency (output
corrected).
The input saving measure shows how large a proportion of the
observed input would have been necessary for the output quantity
observed if the unit in question had been moved to the efficient
frontier. The output increasing efficiency measure compares the
actual output produced to that of a unit at a point on the
production frontier that uses the same amount of input. These
measures are such that the efficient units will have a value of 1
and the inefficient ones will be less than 1. As an example, a
point such as J in Fig. 1 will, under VRS be input saving efficient
since the efficiency measure is Xj/XI = 1. Point K will be both
input saving and output increasing inefficient since Xs/X K < 1
and YK/YL < 1. When technology is CRS, the input saving
efficiency measure coincides with the gross scale efficiency. This
can be seen in Fig. 1 for point K where both measures are
calculated as XI/XK.
Once input saving, output increasing and gross efficiencies are
obtained, pure scale efficiencies are calculated as in (iv) and (v)
above (E4 = E3/Ea and E5 = E3/E2).
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Efficiency of trucks 395
Scale properties, for a unit i, are expressed as follows, see
[7]:
Eli > g2i indicates that the unit is performing with
increasing returns to scale Eli < E2i indicates that the unit is
performing with decreasing returns to scale Eli = g2i Indicates
that the unit is performing with constant returns to scale.
2.1. Computation of the efficiency scores
Compared to Farrell's approach, DEA offers a more operational
framework for the estimation of efficiency; efficiency is
calculated separately and directly for each production unit in
turn, while at the same time the location of the corresponding
linear facets is determined.
Calculating efficiency measures as defined above is trivial as
long as the production activity consists of only 1 input and 1
output. In order to handle more than 1 input/output, it has been
shown, notably in [5], that a linear programming problem (LP) can
be solved for each unit at time.
The input saving measure is found by solving the following
LP-problem for each unit, k, with output Yk and input Xk, to obtain
the input saving measure under VRS (where Ak is a vector containing
the non-negative weights, Akj, which determine the reference
point):
rain Eak (1)
Ak
subject to the following restrictions
y.k
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396 Lennart Hjalmarsson and James Odeck
When efficiency is measured along a ray from the origin a micro
unit may turn out as fully efficient, although it is not fully
efficient in the sense that it is dominated by other units
(regardless of assumption about scale property). In empirical
applications this can be controlled for by inspection of the slack
variables.
The output increasing efficiency measure is achieved by
restricting the reference point on the unknown frontier to
employing the same amount of input(s) as observed for unit k. The
efficiency scores are obtained by the following LP-problem:
1 max ~72k w.r.t (2)
1 N (2a) EzkYrk~ zN,~kjXij, i = 1 , . . . ,n (2b)
zN,~kj = 1 (2c)
),ej 1> 0, j = 1, . . . , N (2d)
where E2k is the output increasing efficiency measure for unit
k. The rest of the variables are defined as in (1-ld). Restriction
(2a) states that the efficiency corrected volume of output
[(1/E2k)Yrk] must be less than or equal to the amount of output
produced by the reference unit. Restriction (2b) states that the
amount of inputs used by unit k must at least equal the amount of
input used by the reference unit. Restrictions (2c) and (2d) are
interpreted as in (lc) and (ld). Observed outputs, r = 1 , . . . ,
m, of unit k will now be efficiency adjusted proportionally upwards
to be less or equal to output at the frontiers reference point,
where at least one output equals the reference point.
Since scale inefficiency is due to either decreasing or
increasing returns to scale, one can easily determine the case by
inspecting the sum of weights, S:
s = (3)
for the E1 calculations with CRS technology. If this sum is less
than one we have increasing returns to scale (both at K and at the
adjusted point J at the VRS frontier), and if it is larger than one
we have decreasing returns to scale.
Banker et al. [8] defines a specific scale measure termed Most
Productive Scale Size (MPSS). MPSS is obtained as:
Mess = E3 (4) ~_dN_-i Akj
The relation between the actual scale and Mess is that for units
exhibiting increasing returns to scale, input saving efficiency
improvement will move the unit further away from MPSS. The
implication is that the units are encouraged to increase their
activities rather than reduce them.
Some caution is in order concerning DEA as a technique for
efficiency measurement. Since DEA yields relative efficiency
measures and defines a unit (in this case a truck) as ineffective
by comparing combinations of input and output with other units,
units operating with input-output quantities sufficiently far from
the other units at both ends of the size distribution will be
identified as efficient due to the lack of comparable units.
Problems of this kind are, however, minimal if the sample size is
large in comparison to the number of inputs and outputs. This is
because larger samples decrease the average level of efficiency,
due to the positive probability of including more efficient
outliers in the sample.
3. THE DATA
For the analysis we have used 2 sets of data available in the
PRA's data base involving trucks of
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Efficiency of trucks 397
vintage 1983-1985. The data are collected and monitored by the
regional branches according to a standard set up by the PRA.
The first data set is the yearly accounts of costs associated
with the running of each truck. The following comprises this data
set:
- - model year (vintage) of the truck - - make and model of the
truck - - capacity of the truck in tons - - region of operation - -
wage costs of the driver per year - - fuel costs of the truck per
year - - cost of rubber accessories (tires, belts etc.) for the
truck per year - - maintenance costs for the truck per year
(excluding rubber maintenance equipment).
All costs are expressed in Norwegian currency (NOK). The
capacity of trucks is, however, fixed (all at 16.5 ton) for the
whole fleet of trucks. These data are available for 72 units.
The second data set contains tasks performed by each of the 72
trucks. This data set consists of:
- - transportation work in kilometers per year - - volume
transported in cubic meters per year - - effective hours in
production per year (i.e excluding stoppage time).
3.1. Inputs The accounting data given above cover all the costs
related to running a truck with the exception
of fixed costs. Fixed costs are not registered and it is
difficult to obtain them. The insurance premium, being one of the
major components of fixed costs could have been used as a proxy.
However the insurance companies informed us that a difference of 3
yr (note that our data comprise of trucks of model (1983-85) is
insignificant when considering insurance premiums. Therefore the
fixed costs are excluded.
The driver's wage is measured as the annual driver's wage given
in the accounts. Each machine employs only one type of labour (the
drivers) and hence the problem of heterogeneity does not arise.
Since the machines are publically owned, the drivers are on the
same wage scale. The price of labour is therefore not expected to
vary by units due to variations in local labour markets.
Concerning fuel, although we have no liter prices, the
information gathered indicates no variation in price per liter
across units or regions.
The cost of rubber accessories (tires etc.) is registered
separately from the maintenance costs. For an ordinary vehicle,
these 2 cost components should be aggregated together. Itere, they
are kept as separate inputs because rubber accessories for trucks
tend to vary according to kilometers covered and most importantly,
volume of the mass transported.
There is no reason to expect variation in maintenance and rubber
costs across units and regions since prices for most of the
services are standardized throughout. The analysis is therefore
carried out with 4 inputs, wage (W), fuel (F), rubber (R) and
maintenance (M). As is evident from Table 1, wages are by far the
largest single input followed by maintenance.
3.2. Output The traditional output measure of transportation
work is the transported volume of mass times
kilometer, i.e. tonkm. The trucks belonging to PRA perform
several tasks both in maintenance and construction of roads. These
trucks generally transport massess during construction but they
also plow snow during the winter season. The volume of mass
transported (snow plowed) is, however, not registered in
maintenance operations. Thus, tonkm cannot be applied as an output
measure.
Therefore, we have chosen to use 2 alternative output measures:
Total transport distance (KM) and effective hours in production
(EH). While the latter measure reveals the degree of capacity
utilization of the trucks the first measure is a more direct output
measure.
An overview of the input and output variables used is given in
Table 1.
C~OR 23:4-G
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398 Lennart Hjalmarsson and James Odeck
Table 1. Summary statistics of inputs and outputs
In NOK1000 W F R M EH KM
Sum 20718603 3112910 4616280 6742941 130888 2555128 Avg 287758
432354 64115 93652 18t8 35488 Min 4293 7051 11441 12789 252 8158
Max 553084 114699 146389 247478 3263 76537 S.D. 100606 20715 29056
53386 582 15982
4. EMPIRICAL RESULTS
For each truck in the sample, the LP-problems (1) and (2),
outlined in Section 2, were solved with and without constraint (lc)
and for the 2 alternative output measures.
4.1. Efficiency results We use the Farrell measures to compare
observed performance with potential frontier perfor-
mance, keeping the factor inputs or outputs as observed. The 3
types of efficiency we calculate in this paper are those
illustrated in Fig. 1.
The distribution of E 1 (VRS) for both the alternative measures
of output are presented in Figs 2 and 3. Each histogram in Figs 2
and 3 represents a unit (truck). The size of the truck, as measured
by output is represented by the width of the histogram normalized
by the output shares.
The input saving efficiency distribution E1 (VRS) when output is
measured by kilometer transportation work, presented in Fig. 2,
shows that the most efficient trucks represent about 25% of total
output. The efficiency values then decrease evenly down to about
0.6 then continue falling rapidly to the least efficient unit with
an efficiency value of 0.36.
For effective hours in production (EH) as an output measure, the
values of E1 (VRS) in Fig. 3 indicate that the most efficient
trucks represent about 30 of total output. Compared to KM-output,
the efficiency values fall at a slower pace and ending at the least
efficient truck, measuring 0.63 and, representing about 2% of the
total output. In total, there are 13 efficient trucks under
KM-output as compared to 24 under EH as output measure.
A summary of results for all the computations using the two
alternative output measures are given in Tables 2 and 3.
Consider first the input saving efficiency measure when variable
returns to scale technology is imposed, i.e El in Tables 2 and 3.
This measure indicates the input saving potential for the
individual truck had frontier technology been employed. The results
in Table 2 show that if frontier technology
l0' 0.9
0.8
0.7
0.6
0.5.
0.4.
0.3.
0.2.
0.1
E 1
10 20 30 40 50 60 70 80 90 Output shares
100 -~ %
Fig. 2. The distribution of E~ - VRS with KM as output
measure.
-
Efficiency of trucks
1.0t El
0.9 0.8
0.7
0.6
0.5
0.4 0.3
0.2 0. : : .'-
0 I 10 20 30 40 50 60 '70 80 90 100 Output shares
Fig. 3. The distribution of E I - VRS with EH as output
measurc.
%
399
had been imposed, the average truck and the least efficient
truck could have covered the observed annual distance with only 76
and 36% of the inputs, respectively.
The values in Table 3 indicate that there is potential for input
saving of 12% for the average truck, i.e. the average truck could
have managed the observed annual effective hours in production with
only 88 % of the inputs (i.e wage, fuel, rubber and maintenance) if
the frontier technology had been employed. The least efficient
truck could have managed its observed output with only 64% of the
observed inputs had it adopted the frontier technology, i.e. the
potential for input saving achieved by adopting frontier technology
is 36% for the least efficient truck.
Consider now E2 which is the ratio of observed output to
potential frontier output, keeping the level of input unchanged.
Table 3 shows that the outputs for the average and the least
efficient trucks could have been increased by 11 and 47/0
respectively had frontier technology been employed. When the output
specification is changed to annual kilometers travelled, these
measures are at 23.5 and 170% for the average and the least
efficient truck, respectively.
Turning to the gross scale efficiency measure (E3), which can
also be interpreted as an input saving efficiency measure for the
constant returns technology (see Section 2), we find the values to
be lower than those of Ea and E2. The potential saving assuming CRS
technology are always greater than potential savings assuming a VRS
technology, simply because the envelope, under a VRS assumption,
will wrap data more closely (i.e. more units are efficient/define
the envelope) than under a CRS assumption.
Table 2. Summary statistics for efficiency measures and scale
indicator (effective hours in production as output measure)
E1 E2 E3 E4 E5 Scale MPSS
Mean 0.88 0.90 0.82 0.93 0.91 1.51 0.70 Min 0.64 0.68 0.55 0.58
0.58 0.23 0.20 Max 1.00 1.00 1.00 1.00 1.00 3.46 2.40 S.D. 0.10
0.09 0.12 0.08 0.08 0.71 0.47 Weighted mean 0.89 0.90 0.82 0.92
0.90 1.64 0.83
Table 3. Summary statistics for efficiency measures and scale
indicator (distance in km as output measure)
El E2 E3 E4 E5 Scale MPSS
Mean 0.76 0.81 0.64 0.85 0.79 1.36 0.65 Min 0.36 0.37 0.29 0.56
0.50 0.26 0.18 Max 1.00 1.00 1.00 1.00 1.00 3.45 3.17 S.D. 0.18
0.16 0.17 0.13 0.13 0.66 0.55 Weighted mean 0.80 0.84 0.67 0.84
0.80 1.59 0.88
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400 Lennart Hjalmarsson and James Odeck
Input and output adjusted pure scale efficiencies, E4 and Es,
are obtained by dividing E3 by E 1 and E2 respectively. The tales
depict that these scale efficiency measures follow the same pattern
as the other 3 measures of efficiency under the 2 alternative
measures of output. There is obviously no severe scale efficiency
problem in this industry. Technical inefficiency accounts for the
largest potential of efficiency improvement.
When less than one, the scale indicator "scale", in both Tables
2 and 3 indicates an output smaller than the optimal scale, but
larger than the optimal scale when it is larger than one. The
results in the tables indicate that an average truck is larger than
the optimal size. This implies that an average truck will be more
productive had the unit been smaller, i.e. the utilized capacity of
an average truck is too large relative to the tasks that it
performs irrespective of output specification. On the other hand,
the magnitude of this efficiency loss is fairly small as indicated
by the small difference between the gross scale efficiency, E3, and
the pure scale efficiencies, E 4 and Es.
The results of the MPSS measures in Tables 2 and 3 show that the
optimal level of inputs for an average truck should be smaller than
observed, i.e. 65 and 70% of the observed input for KM and EH as
output measures respectively.
These unweighted figures are averages that exert equal
importance to small and large units. In order to obtain a proper
picture of the stock of trucks as a whole weighting the different
results with some measure of size is required. In Tables 2 and 3
the output related measures i.e. E2 and Es, have been weighted with
total output. The input related measures, i.e. E 1 and E4, have
been weighted with total input while E3 and S are weighted with
total output. The tables reveal that the weighting improves the
average efficiencies and scale but only slightly and not
consistently.
The following conclusions can be drawn. First, there is a
notable potential for efficiency gains among trucks due to
technical inefficiency, much less so due to scale inefficiency.
Second, since we are comparing observed performance with
potential frontier performance keeping the inputs or outputs as
observed, the difference in potential efficiency gains is present
between technologies. On average E2 > El, implying decreasing
returns to scale for the average unit in the sample; see [7]. This
observation is consistent with the mean of scale measures which are
found to be greater than 1.
Third, the values of efficiencies depend upon the choice of
output measure. On average measuring output by effective hours
gives a higher level of efficiency measure in comparison to
distance in kilometers. The explanation for this is that the
effective hours in production are highly correlated to wages (which
is also the largest input) as opposed to distance driven in
kilometers. We note that the use of fuel and rubber varies in the
opposite direction i.e. more with distance driven than with
effective hours in production.
4.2. Potential efficiency gains To measure the input saving and
output increasing potential for this fleet of trucks as a
whole,
sector efficiency measures t may be used. These measures are
defined as follows:
I1- ZsyJ (5) Yl
Zs e2j(t) where
I1 is the output increasing potential for the fleet of trucks yj
is output for truck j E2j is output increasing efficiency measure
for truck j t is technology (either CRS or VRS)
I2 ~-'dxijElj(t) (6) -- ~ xo"
tin [9] the input and output saving potentials for the whole
sector are calculated as individual measures by entering the
average as a unit. These measures are termed structural efficiency
and are denoted by Si. To avoid confusion in calculation, we denote
the measure applied in this paper by Ii.
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Efficiency of trucks 401
where
12 is the input saving potential for the fleet of trucks x/j is
input i for truck j Elj is the input saving efficiency (VRS) for
truck j.
Equation (5), thus, measures observed output in relation to
potential output, while (6) measures potential input in relation to
observed input. The percentage by which total output can be
increased is then calculated as (100/I1- 1)100. The percentage
measure for input saving potential is calculated as (1 - 12)100.
The values obtained for 11 and 12 are given in Table 4.
On average, we find that when measured by effective hours in
production (EH), output could be increased by 25 and 12.4%o for CRS
and VRS technologies respectively. When output is measured by
transportation kilometers (KM) the potential for increasing output
is 59 and 23% for CRS and VRS technologies respectively. The
difference between technologies is quite large, 12.6% for EH and
36,/o for KM. Comparing the 2 alternative output measures, the
values for EH are higher than the values for KM. This implies that
kilometers as an output measure yields lower total gains.
When CRS is imposed, smaller gains are obtained in comparison to
VRS independent of output measure. This latter observation conforms
with our previous observation that the average unit does not
operate at constant returns to scale (in fact at decreasing returns
to scale).
The potential input savings, 12, when technology is VRS are
about 22 and 12% for KM and EH respectively. As the results
illustrate, the effect of different factor proportions on input
savings is rather small. Once again KM yields lower gains. In terms
of levels, the input potential (VRS) for savings is greater than
the potential increase in output.
4.3. Sensitivity analysis How robust are the efficiency scores
with regard to output measures and technology assumption.
One measure of robustness is the extent of similarity in ranking
i.e. the correlation between the efficiency scores for different
model specifications. Therefore, Spearman's ranking correlation
coefficient for pairwise comparisons of different model
specifications was calculated.
In general, the rank correlation coefficient is fairly high,
about 0.75, for comparisons between CRS and VRS technology for the
same output measure and efficiency measure. On the other hand,
there is only a weak correlation in ranking between the 2 output
measures, with the same technology. To take one example, in the CRS
case the rank correlation coefficient for a comparison of the E1
measure for the 2 output measures, EH and KM, is 0.24. Thus, it
matters a lot for the efficiency ranking which output measure is
chosen.
4.4. The importance of background factors 4.4.1. The
significance of the brand type and vintage of the trucks. The brand
type of the trucks is
also of interest. Our data set provides this piece of
information. Out of the 72 trucks analyzed there were 54 Volvos, 9
Saab Scanias, 3 Mercedes Benzes and 3 M.A.Ns. Thus, trucks of the
Volvo type dominate the sample.
In testing the significance of brand type, Volvo trucks were
compared to a set of all the other vehicles in the group. A
Mann-Whitney test was then carried out to compare the efficiency
rating of
Output = KM
Output = EH
Tab le 4. Sector eff ic iency measures
11 /2
t = CRS 0.63 t = VRS 0.81
t = CRS 0 .80 t = VRS 0,89
0.78 i = W 0.78 i = F 0.76 i = R 0.76 i = M
0.88 i = W 0.87 i = F 0.87 i = R 0.88 i = M
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402 Lennart Hjalmarsson and James Odeck
the 2 populations. The results indicate no influence of make on
efficiency level irrespective of the choice of output variable.
A common assumption is that old trucks require more inputs
(repair, lubrication, consumes more fuel etc.) in producing the
same output than newer vehicles. Our data comprise of trucks of 3
different age groups: those produced and set into operation in
1983, 1984 and 1985. A Mann- Whitney test on the influence of age
on performance was also carried out.
The result shows that the model of truck does not significantly
influence vehicle performance. No test could be rejected at the 10%
significance level. An obvious reason here is that a 3yr age
difference is not long enough period for trucks to perform
differently on the basis of age.
4.4.2. Regional comparison of efficiency measurement. When
investigating the performance of trucks in the road sector and when
these trucks are both used in maintenance and construction, some
regional aspects need to be considered. For a start, in maintenance
services such as snow plowing there will always exist differences
across regions for instance in terms of cubic meters of snow plowed
annually. This is mainly due to differences in climatic conditions.
As regards construction, the distance driven by trucks depends on
the amount of mass being transported and their place of disposal.
As an example, regions along the Norwegian coast are mountainous
and hence rock blasting is more common. Tunnel construction is
common in these areas. This implies that a much larger amount of
mass transported here than in other regions. One might then expect
regional differences in efficiency.
The data set allows for regional comparisons. For this purpose
we have aggregated the data to only 2 regions as follows: regions
along the coast which also have relatively low annual snow fall and
the non-costal regions with relatively high amounts of snow fall.
Again, a Mann-Whitney test is performed. The results presented in
Table 5 indicate that the observed differences in efficiency
between regions are all significant at the 1% level for measures
apart from E1 (VRS) and E2 (VRS) when output is KM, and E1 (VRS)
when output is EH. These results indicate that the region factor is
important when measuring efficiency across regions.
The figures in Table 5 show that when output is measured by KM,
the mean efficiency in the coastal regions are higher than in the
inland regions. When output is measured by effective hours worked
the result is the reverse. An explanation here is that trucks are
disposed differently in the different regions, i.e. in costal
regions they do more of mass transportation while they perform more
of snow plowing in the inland regions.
4.5. The frontier units A main purpose of calculating efficiency
scores is to get ideas for improving the performance of
the ineffective units relative to the best practice units. It
is, therefore, quite important that the best practice units and
their properties are revealed. In Table 6 the frequency of
occurrence on the frontier by efficiency and output measure is
presented.
Let us first look at the dominating units relative to the output
measure. When output is measured by KM, 3 units dominate (unit 28,
54 and 71) under all technology restrictions. However, when VRS
technology is imposed units 41, 45 and 50 also become dominant.
Changing output measure to EH increases the number of dominant
units (and also the number of efficient ones) under all
specifications of technology. The most dominant units are 8, 24, 54
and 63. It is only 1 unit that is dominant under both output
measures (unit 54). Again there are more frontier units when
VRS
Table 5. Test of the impact of regional differences on
efficiency scores
EH KM Coastal Inland Coastal Inland
~'1 (CRS) Mean efficiency 0.84 0.79 0.61 0.69 Sign. level 0.0763
0.0000
E~ (VRS) Mean efficiency 0.90 0.85 0.74 0.82 Sign. level 0.1556
0.3715
E~ (VRS) Mean efficiency 0.91 0.87 0.78 0.85 Sign. level 0.1407
0.0304
-
Efficiency of trucks
Table 6. Frequency of units on the frontier
403
Output KM EH Size
E l E l E2 Unit CRS VRS VRS Sca le E l E l Ez Sca le EH Kid
2 - - - - - - 1 .53 3 2 2 1 .00 1810 21106
5 - - 10 5 0 .35 14 5 5 1 .00 525 9117 8 - - - - 1 .09 34 28 27
- - 1 .00 1810
14 - - - - - - 0 .26 6 2 2 1 .00 1339 14100
19 - - - - - - 0 .98 - - 1 1 0 .50 1151 20694
20 - - 8 11 1 .85 - - - - - - 1 .06 1855 38909
24 3 16 - - 1 .00 25 12 13 - - 1 .00 1679
25 - - 1 1 1 .85 - - 1 1 2 .46 3133 76537 26 - - - - - - 0 .66 -
- 3 4 1 .99 2382 36893
28 24 4 6 2 .16 - - - - - - 2 .21 2155 51204 30 - - - - - - 1
.40 8 7 6 1 .00 1941 29488
40 - - - - - - 1 .53 - - - - - - 0 .99 1725 34276
42 - - - - - - 1 .14 - - 1 1 1 .78 2149 41527
45 - - 18 22 3 .50 - - - - 1 .50 2308 73520 46 - - 16 1 0 .39 -
- 3 1 0 .30 252 8158
47 - - - - - - 0 .87 6 7 9 1 .00 1911 43799
48 - - 13 7 1 .00 - - 3 4 1 .63 2942 72412
50 - - 17 23 2 .87 - - 1 1 1 .83 3263 63372
51 - - - - - - 2 .30 37 48 - - 1 .92 3245
52 - - - - 1 .00 2 7 2 1 .00 1962 29335
54 67 60 61 1 .00 48 25 22 - - 1 .00 360
62 - - - - - - 0 .72 2 6 1 1 .00 1462 23123 63 - - - - 0 .82 42
36 28 - - 1 .00 1430
71 28 39 47 1 .00 - - 8 2 2 .60 2982 75644
72 - - 1 2 3 .48 - - - - - - 1A9 1793 73321
AVG 1817.8
technology is imposed. A clear observation from Table 6, which
is also mentioned in the previous section, is that the composition
of units on the frontier varies with the output specification.
Consider now the units on the frontier, given in Table 6,
relative to their size measured by outputs. The units that dominate
in all specifications and output measures differ when size is
considered. As an example, units 54 and 71 dominate when KM is
specified as output measure. Their sizes by the KM-measure reveal
that while unit 54 is smaller than the average unit, unit 71 is
twice the size of the average unit. It is also noted that unit 40
although efficient, does not appear as best practice for all other
units than itself. This is one of the largest units in the
sample.
In terms of optimality with respect to scale, most dominant
units are scale optimal, i.e. have scale values of 1. This
observation being irrespective of the choice of output. It is also
observed that there exist a few dominant units that operate under
Strong increasing returns to scale. These are 5, 14 and 46 when the
KM-output measure is used and 19 and 46 when the output measure is
EH. Unit 45 is the only one among the dominant ones that operates
with strong decreasing returns to scale, and only when the
KM-output measure is used.
5. C O N C L U D I N G R E M A R K S
The results received indicate substantial variations in
efficiency across trucks. An average truck is found to have an
effciency score of 0.76 and 0.88 when the output measure used in
kilometers (KM) and effective hours (EH) respectively.
The potential for increasing output/ saving input is measured by
/1 and 12 underlines the importance of technology when dealing with
trucks. An imposition of the VRS technology when output is measured
by EH would increase output by 25% as opposed to 12.4% when CRS is
imposed. An average unit is, however, found to exhibit decreasing
returns to scale technology.
Appropriate measures of output are important when dealing with
trucks involved in more than one type of operation. The results
reached here indicate that when all units are considered as one
group the number of kilometers as an output measure generates lower
efficiency measures in comparison to effective hours in production.
When trucks are classified according to their regions this
difference has, however, a second dimension. KM are found to
generate high scores in inland regions while EH generate higher
scores in the coastal regions. The difference is due to the
-
404 Lennart Hjalmarsson and James Odeck
composition of operations i.e. trucks in the inland regions
undertake more snow plowing than those in the coastal regions where
there is less snow and more mass transportation.
Neither the make of the truck nor the model were found to
influence performance. Regarding size of trucks measured in terms
of annual output, the influence on efficiency measures were slight
when output is measured by DM and insignificant when measured by
EH.
In summary, it can be concluded that there is substantial
variation in the performance of trucks and that there is scope for
eradicating some of the causes of the inefficiency. For the latter,
the most useful information relates to the region in which the
truck operates, the output measure to be used and, the units that
define the frontier and their relative weights.
The results arrived at here have a number of policy
implications. The efficiency results obtained by DEA methodology
yield values of inputs, outputs and scale which, in principle, an
agency should be able to achieve. For example in Section 4.1, we
showed that if the frontier technology had been employed the
average truck could have sustained the annual effective hours in
production with only 88% of the input (i.e. wage, fuel, rubber and
maintenance). Although the adoption of frontier technology would
bring the truck to the frontier, complete adjustment may not be
possible because some factors that influence performance may not be
under the control of the agency concerned. Nevertheless, while DEA
does not provide a precise mechanism for achieving efficiency, it
does help in quantifying the magnitude of change required to make
the inefficient units (trucks) efficient.
The tasks, thus, involve finding explanations for variation in
performance. One way to go about this is to inspect the key
characteristics of each frontier truck and then compare it to the
inefficient trucks that it defines the frontier for. The agency
with inefficient trucks can then learn from the frontier trucks
and/or explain the causes of own inefficiency. The central
authority (PRA) could also isolate the agencies that use public
funds inefficiently from those that perform satisfactorily. More
administrative attention may then be paid to those that perform
poorly.
The Public Roads Administration of Norway lacks market prices
for its services. A common way of measuring productivity in public
sectors, when market prices are lacking, is by dividing physical
output by physical input. However, when there are many outputs and
inputs, managers of public sector agencies prefer multiple
output/input ratios, each of which tells a different story. In this
case no robust conclusions can be drawn on the performance on any
particular agency, in comparison to others of the same nature. It
is in this respect that the DEA approach used in this study could
assist in aggregating several measures so that a single indicator
for an agency's performance is obtained.
Acknowledgement--Financial support from HSFR and Jan Wallander
Research Foundation is gratefully acknowledged.
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